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Groups and FieldsChallengeDirect Products and Finite Abelian Groups

Direct Products and Finite Abelian Groups · Challenge problem

In the direct product Z12×Z18\mathbb Z_{12} \times \mathbb Z_{18}, consider the quotient (Z12×Z18)/⟨(2,3)⟩(\mathbb Z_{12}\times\mathbb Z_{18})/\langle(2,3)\rangle. What is the largest order of an element in this quotient?